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The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials.
A generalized guided monte carlo algorithm
Alan M. Horowitz · 1991
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The notion of error in langevin dynamics. i. linear analysis
Bimal Mishra and Tamar Schlick · 1996
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Geometric l 2 and l 1 convergence are equivalent for reversible markov chains
Gareth O. Roberts and Richard L. Tweedie · 2001
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One-shot coupling for certain stochastic recursive sequences
Gareth O. Roberts and Jeffrey S. Rosenthal · 2002
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Stochastic Hamiltonian systems: exponential convergence to the invariant measure, and discretization by the implicit Euler scheme
Denis Talay · 2002
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Transportation cost-information inequalities and applications to random dynamical systems and diffusions
Hacène. Djellout, Arnaud Guillin, and Li-Ming Wu · 2004
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Concentration inequalities for euler schemes
Florent Malrieu and Denis Talay · 2004
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Stochastic Numerics for Mathematical Physics
Grigori N. MilsteinMichael V. Tretyakov · 2004
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An efficient sampling algorithm for variational monte carlo
Anthony Scemama, Tony Lelièvre, Gabriel Stoltz, Eric Cancès, and Michel Caffarel · 2006
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Accurate sampling using langevin dynamics
Giovanni Bussi and Michele Parrinello · 2007
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Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
Frederic Hérau · 2007
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Hypocoercivity for kinetic equations with linear relaxation terms
Jean Dolbeault, Clément Mouhot, and Christian Schmeiser · 2009
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Ricci curvature of markov chains on metric spaces
Yann Ollivier · 2009
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Hypocoercivity
Cédric Villani · 2009
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Optimal transport, old and new
Cédric Villani · 2009
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Trend to equilibrium and particle approximation for a weakly selfconsistent vlasov-fokker-planck equation
François Bolley, Arnaud Guillin, and Florent Malrieu · 2010
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Pathwise accuracy and ergodicity of metropolized integrators for sdes
Nawaf Bou-Rabee and Eric Vanden-Eijnden · 2010
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On the long time behavior of the TCP window size process
Djalil Chafaï, Florent Malrieu, and Katy Paroux · 2010
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Curvature, concentration and error estimates for markov chain monte carlo
Aldéric Joulin and Yann Ollivier · 2010
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Duality on gradient estimates and Wasserstein controls
Kazumasa Kuwada · 2010
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Free energy computations: A mathematical perspective
Tony Lelièvre, Mathias Rousset, and Gabriel Stoltz · 2010
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Quantitative bounds for markov chain convergence: Wasserstein and total variation distances
Neal Madras and Deniz Sezer · 2010
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MCMC using Hamiltonian dynamics
Radford M. Neal · 2010
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Statistical mechanics theory and molecular simulation
Mark E. Tuckerman · 2010
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A patch that imparts unconditional stability to explicit integrators for langevin-like equations
Nawaf Bou-Rabee and Eric Vanden-Eijnden · 2012
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Convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation
Yin Tat Lee and Santosh S. Vempala · 2018
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Dimensionally Tight Bounds for Second-Order Hamiltonian Monte Carlo
Oren Mangoubi and Nisheeth K. Vishnoi · 2018
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Hypocoercivity in metastable settings and kinetic simulated annealing
Pierre Monmarché · 2018
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The zig-zag process and super-efficient sampling for Bayesian analysis of big data
Joris Bierkens, Paul Fearnhead, and Gareth Roberts · 2019
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Bounding the error of discretized langevin algorithms for non-strongly log-concave targets
A. Dalalyan, Lionel Riou-Durand, and Avetik G. Karagulyan · 2019
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Degenerate fokker–planck equations: Bismut formula, gradient estimate and harnack inequality
Arnaud Guillin and Feng-Yu Wang · 2012
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Rational Construction of Stochastic Numerical Methods for Molecular Sampling
Benedict Leimkuhler and Charles Matthews · 2012
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Analysis and geometry of Markov diffusion operators
Dominique Bakry, Ivan Gentil, and Michel Ledoux · 2014
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Positive curvature and hamiltonian monte carlo
Christof Seiler, Simon Rubinstein-Salzedo, and Susan Holmes · 2014
Cited alongside, same era.
On ℋ 1 \mathcal{H}^{1} and entropic convergence for contractive PDMP
Pierre Monmarché · 2015
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Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo
Alain Durmus, Umut Simsekli, Éric Moulines, Roland Badeau, and Gael Richard · 2016
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High-dimensional bayesian inference via the unadjusted langevin algorithm
Alain Durmus and Éric Moulines · 2019
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Log-concave sampling: Metropolis-hastings algorithms are fast
Raaz Dwivedi, Yuansi Chen, Martin J. Wainwright, and Bin Yu · 2019
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Couplings and quantitative contraction rates for langevin dynamics
Andreas Eberle, Arnaud Guillin, and Raphael Zimmer · 2019
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Non-asymptotic error bounds for scaled underdamped Langevin MCMC
Tim Zajic · 2019
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On the Effectiveness of Richardson Extrapolation in Machine Learning
Francis Bach · 2020
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Coupling and convergence for Hamiltonian Monte Carlo
Nawaf Bou-Rabee, Andreas Eberle, and Raphael Zimmer · 2020
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Fast mixing of metropolized hamiltonian monte carlo: Benefits of multi-step gradients
Yuansi Chen, Raaz Dwivedi, Martin J. Wainwright, and Bin Yu · 2020
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On sampling from a log-concave density using kinetic langevin diffusions
Arnak S. Dalalyan and Lionel Riou-Durand · 2020
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Arnaud Guillin and Pierre Monmarché · 2020
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Pierre Monmarché · 2020
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Kinetic walks for sampling
Pierre Monmarché · 2020
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On the limitations of single-step drift and minorization in markov chain convergence analysis, 2020
Qian Qin and J. Hobert · 2020
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Hamiltonian Assisted Metropolis Sampling
Zexi Song and Zhiqiang Tan · 2020
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Is there an analog of Nesterov acceleration for gradient-based MCMC?
Yi-An Ma, Niladri S. Chatterji, Xiang Cheng, Nicolas Flammarion, Peter L. Bartlett, and Michael I. Jordan · 2021
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